By beheading Nathanos, she just served as his taxi to bring him back to his Dark Lady.
The amount of enemies remains the same.
If she had imprisoned him in the Warden Jail, Nathanos would be punished by being separated from Sylvanas (the one person he cares about) and the enemy forces would be weakened.
The characters in the game do not know about the Shadowlands.
The whole reason Tyrande showed up, other than to enjoy a justified beheading, was to grill Nathanos for information about where Sylvanas and her kidnapping victims are.
And Nathanos told her. Tyrande got exactly what she wanted and barely needed to interrogate him at all.
At the time Tyrande doesn’t seem to know about the hole in the afterlife. And Nathanos was just being cryptically useless, so naturally she killed him.
But it does at least remove him from this world. His soul goes to the Maw, but he doesn’t have a body here anymore.
The leaders and we, the players, don’t learn about all the shadowlands/maw stuff until Bolvar summons us to the frozen throne to open a pathway using the shattered helm.
So, as I see it, Tyrande had no idea about the sending him to the Maw stuff
Yes, so she did know that, as he claims, he will reunite with Sylvanas if he dies, but I don’t think she cared.
The fact she got the information about the shadowlands and where the kidnapping victims are is the true victory here. Nathanos dying is not a victory, he could have just killed himself before anyone arrived if he wanted to.
Also Sylvanas last said to Nathanos before this that he needs to figure out how to kill Bwomsamdi and to not show his face again until he has. But he hasn’t. I don’t think Sylvanas will be all that excited to see Nathanos in the maw after having failed her twice in a row.
I wouldn’t be surprised if next time we see him it’s a Lady Priscilla Ashvane situation where he’s been put in the body of some horrible abomination due to his failures and overestimating his value.
I mean if he really wanted to die he could have just killed himself. There would be no reason he would need to taunt Tryande into it so he was probably just bluffing/trolling. She got what she wanted which was Sylvanas’ location.